- #1
azizz
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Homework Statement
Proof: [tex] \lambda_{\max}(A+B) \leq \lambda_{\max}(A) + \lambda_{\max}(B) [/tex]
Homework Equations
Hint from exercise: [tex] \lambda_{\max}(A)=\max_{\|x\|=1} x^*Ax [/tex]
The Attempt at a Solution
The problem is that the equation on the left side can not be split. So I tried to write it as follows:
[tex] \max_{\|x\|=1} x^*(A+B)x \leq x^*(A+B)x = x^*Bx + x^*Ax [/tex]
But that don't really helps me and I can't think of an other way to tackle this problem...